@shrawan: If you know that your data contains several outliers, then I guess you should rather try standardization.

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Sometimes perhaps we can take logarithms of input data when they contain order-of-magnitude larger and smaller values. However, since logarithms are defined for positive values only, we need to take care when the input data may contain zero and negative values. You did a very good work on your blog!

Xi, -1 to 1 = The data point i normalized between 0 and 1

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The mean and std dev are definable for any continuous-variable distribution and therefore, regardless of the true underlying distribution, standardization will yield data having a mean of 0 and std dev of 1. There is no assumption that the underlying distribution is Gaussian.

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Xi, 0 to 1 = The data point i normalized between 0 and 1

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This process is sometimes used to make conventional measures more robust, as in the Winsorized variance.

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The z-scores allow us to compare student performance better than the raw marks since they have corrected for the different levels of difficulty of the three tests.

I presume it may distort the correlation between attibutes and therfore corrupt the results. If that’s the case, one has to choose between normalization and standarization for the whole dataset?.

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For readers who are not aware of this technique: “Winsorizing” data simlpy means clamping the extreme values.

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How to standardaise data

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The conclusion from this experiment is that data should be normalized or standardized to remove their scale from your modeling, but both techniques produce identical results to this desired outcome.  However, standardizing is the preferred method because it produces meaningful information about each data point, and where it falls  within its normal distribution, plus provides a crude indicator of outliers (i.e., anything above or below a Z-Score of ±4.

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The diagram below shows the marks obtained by 20 students in a maths test.

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Standardizing a variable is a relatively straightforward procedure. First, the mean is subtracted from the value for each case, resulting in a mean of zero. Then, the difference between the individual's score and the mean is divided by the standard deviation, which results in a standard deviation of one. If we start with a variable x, and generate a variable x*, the process is:

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